xref: /llvm-project/libc/src/math/generic/range_reduction_double_fma.h (revision 51e9430a0c767243411d4b81c284700f89719277) 
1 //===-- Range reduction for double precision sin/cos/tan w/ FMA -*- C++ -*-===//
2 //
3 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4 // See https://llvm.org/LICENSE.txt for license information.
5 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6 //
7 //===----------------------------------------------------------------------===//
8 
9 #ifndef LLVM_LIBC_SRC_MATH_GENERIC_RANGE_REDUCTION_DOUBLE_FMA_H
10 #define LLVM_LIBC_SRC_MATH_GENERIC_RANGE_REDUCTION_DOUBLE_FMA_H
11 
12 #include "src/__support/FPUtil/FPBits.h"
13 #include "src/__support/FPUtil/double_double.h"
14 #include "src/__support/FPUtil/multiply_add.h"
15 #include "src/__support/FPUtil/nearest_integer.h"
16 #include "src/__support/common.h"
17 #include "src/__support/macros/config.h"
18 #include "src/__support/macros/optimization.h"
19 #include "src/math/generic/range_reduction_double_common.h"
20 
21 namespace LIBC_NAMESPACE_DECL {
22 
23 using LIBC_NAMESPACE::fputil::DoubleDouble;
24 
25 LIBC_INLINE unsigned LargeRangeReduction::fast(double x, DoubleDouble &u) {
26   using FPBits = typename fputil::FPBits<double>;
27   FPBits xbits(x);
28 
29   int x_e_m62 = xbits.get_biased_exponent() - (FPBits::EXP_BIAS + 62);
30   idx = static_cast<unsigned>((x_e_m62 >> 4) + 3);
31   // Scale x down by 2^(-(16 * (idx - 3))
32   xbits.set_biased_exponent((x_e_m62 & 15) + FPBits::EXP_BIAS + 62);
33   // 2^62 <= |x_reduced| < 2^(62 + 16) = 2^78
34   x_reduced = xbits.get_val();
35   // x * c_hi = ph.hi + ph.lo exactly.
36   DoubleDouble ph =
37       fputil::exact_mult<SPLIT>(x_reduced, ONE_TWENTY_EIGHT_OVER_PI[idx][0]);
38   // x * c_mid = pm.hi + pm.lo exactly.
39   DoubleDouble pm =
40       fputil::exact_mult<SPLIT>(x_reduced, ONE_TWENTY_EIGHT_OVER_PI[idx][1]);
41   // x * c_lo = pl.hi + pl.lo exactly.
42   DoubleDouble pl =
43       fputil::exact_mult<SPLIT>(x_reduced, ONE_TWENTY_EIGHT_OVER_PI[idx][2]);
44   // Extract integral parts and fractional parts of (ph.lo + pm.hi).
45   double sum_hi = ph.lo + pm.hi;
46   double kd = fputil::nearest_integer(sum_hi);
47 
48   // x * 128/pi mod 1 ~ y_hi + y_mid + y_lo
49   y_hi = (ph.lo - kd) + pm.hi; // Exact
50   y_mid = fputil::exact_add(pm.lo, pl.hi);
51   y_lo = pl.lo;
52 
53   // y_l = x * c_lo_2 + pl.lo
54   double y_l =
55       fputil::multiply_add(x_reduced, ONE_TWENTY_EIGHT_OVER_PI[idx][3], y_lo);
56   DoubleDouble y = fputil::exact_add(y_hi, y_mid.hi);
57   y.lo += (y_mid.lo + y_l);
58 
59   // Digits of pi/128, generated by Sollya with:
60   // > a = round(pi/128, D, RN);
61   // > b = round(pi/128 - a, D, RN);
62   constexpr DoubleDouble PI_OVER_128_DD = {0x1.1a62633145c07p-60,
63                                            0x1.921fb54442d18p-6};
64 
65   // Error bound: with {a} denote the fractional part of a, i.e.:
66   //   {a} = a - round(a)
67   // Then,
68   //   | {x * 128/pi} - (y_hi + y_lo) | <=  ulp(ulp(y_hi)) <= 2^-105
69   //   | {x mod pi/128} - (u.hi + u.lo) | < 2 * 2^-6 * 2^-105 = 2^-110
70   u = fputil::quick_mult<SPLIT>(y, PI_OVER_128_DD);
71 
72   return static_cast<unsigned>(static_cast<int64_t>(kd));
73 }
74 
75 // Lookup table for sin(k * pi / 128) with k = 0, ..., 255.
76 // Table is generated with Sollya as follow:
77 // > display = hexadecimal;
78 // > for k from 0 to 255 do {
79 //     a = D(sin(k * pi/128)); };
80 //     b = D(sin(k * pi/128) - a);
81 //     print("{", b, ",", a, "},");
82 //   };
83 LIBC_INLINE constexpr DoubleDouble SIN_K_PI_OVER_128[256] = {
84     {0, 0},
85     {-0x1.b1d63091a013p-64, 0x1.92155f7a3667ep-6},
86     {-0x1.912bd0d569a9p-61, 0x1.91f65f10dd814p-5},
87     {-0x1.9a088a8bf6b2cp-59, 0x1.2d52092ce19f6p-4},
88     {-0x1.e2718d26ed688p-60, 0x1.917a6bc29b42cp-4},
89     {0x1.a2704729ae56dp-59, 0x1.f564e56a9730ep-4},
90     {0x1.13000a89a11ep-58, 0x1.2c8106e8e613ap-3},
91     {0x1.531ff779ddac6p-57, 0x1.5e214448b3fc6p-3},
92     {-0x1.26d19b9ff8d82p-57, 0x1.8f8b83c69a60bp-3},
93     {-0x1.af1439e521935p-62, 0x1.c0b826a7e4f63p-3},
94     {-0x1.42deef11da2c4p-57, 0x1.f19f97b215f1bp-3},
95     {0x1.824c20ab7aa9ap-56, 0x1.111d262b1f677p-2},
96     {-0x1.5d28da2c4612dp-56, 0x1.294062ed59f06p-2},
97     {0x1.0c97c4afa2518p-56, 0x1.4135c94176601p-2},
98     {-0x1.efdc0d58cf62p-62, 0x1.58f9a75ab1fddp-2},
99     {-0x1.44b19e0864c5dp-56, 0x1.7088530fa459fp-2},
100     {-0x1.72cedd3d5a61p-57, 0x1.87de2a6aea963p-2},
101     {0x1.6da81290bdbabp-57, 0x1.9ef7943a8ed8ap-2},
102     {0x1.5b362cb974183p-57, 0x1.b5d1009e15ccp-2},
103     {0x1.6850e59c37f8fp-58, 0x1.cc66e9931c45ep-2},
104     {0x1.e0d891d3c6841p-58, 0x1.e2b5d3806f63bp-2},
105     {-0x1.2ec1fc1b776b8p-60, 0x1.f8ba4dbf89abap-2},
106     {-0x1.a5a014347406cp-55, 0x1.073879922ffeep-1},
107     {-0x1.ef23b69abe4f1p-55, 0x1.11eb3541b4b23p-1},
108     {0x1.b25dd267f66p-55, 0x1.1c73b39ae68c8p-1},
109     {-0x1.5da743ef3770cp-55, 0x1.26d054cdd12dfp-1},
110     {-0x1.efcc626f74a6fp-57, 0x1.30ff7fce17035p-1},
111     {0x1.e3e25e3954964p-56, 0x1.3affa292050b9p-1},
112     {0x1.8076a2cfdc6b3p-57, 0x1.44cf325091dd6p-1},
113     {0x1.3c293edceb327p-57, 0x1.4e6cabbe3e5e9p-1},
114     {-0x1.75720992bfbb2p-55, 0x1.57d69348cecap-1},
115     {-0x1.251b352ff2a37p-56, 0x1.610b7551d2cdfp-1},
116     {-0x1.bdd3413b26456p-55, 0x1.6a09e667f3bcdp-1},
117     {0x1.0d4ef0f1d915cp-55, 0x1.72d0837efff96p-1},
118     {-0x1.0f537acdf0ad7p-56, 0x1.7b5df226aafafp-1},
119     {-0x1.6f420f8ea3475p-56, 0x1.83b0e0bff976ep-1},
120     {-0x1.2c5e12ed1336dp-55, 0x1.8bc806b151741p-1},
121     {0x1.3d419a920df0bp-55, 0x1.93a22499263fbp-1},
122     {-0x1.30ee286712474p-55, 0x1.9b3e047f38741p-1},
123     {-0x1.128bb015df175p-56, 0x1.a29a7a0462782p-1},
124     {0x1.9f630e8b6dac8p-60, 0x1.a9b66290ea1a3p-1},
125     {-0x1.926da300ffccep-55, 0x1.b090a581502p-1},
126     {-0x1.bc69f324e6d61p-55, 0x1.b728345196e3ep-1},
127     {-0x1.825a732ac700ap-55, 0x1.bd7c0ac6f952ap-1},
128     {-0x1.6e0b1757c8d07p-56, 0x1.c38b2f180bdb1p-1},
129     {-0x1.2fb761e946603p-58, 0x1.c954b213411f5p-1},
130     {-0x1.e7b6bb5ab58aep-58, 0x1.ced7af43cc773p-1},
131     {-0x1.4ef5295d25af2p-55, 0x1.d4134d14dc93ap-1},
132     {0x1.457e610231ac2p-56, 0x1.d906bcf328d46p-1},
133     {0x1.83c37c6107db3p-55, 0x1.ddb13b6ccc23cp-1},
134     {-0x1.014c76c126527p-55, 0x1.e212104f686e5p-1},
135     {-0x1.16b56f2847754p-57, 0x1.e6288ec48e112p-1},
136     {0x1.760b1e2e3f81ep-55, 0x1.e9f4156c62ddap-1},
137     {0x1.e82c791f59cc2p-56, 0x1.ed740e7684963p-1},
138     {0x1.52c7adc6b4989p-56, 0x1.f0a7efb9230d7p-1},
139     {-0x1.d7bafb51f72e6p-56, 0x1.f38f3ac64e589p-1},
140     {0x1.562172a361fd3p-56, 0x1.f6297cff75cbp-1},
141     {0x1.ab256778ffcb6p-56, 0x1.f8764fa714ba9p-1},
142     {-0x1.7a0a8ca13571fp-55, 0x1.fa7557f08a517p-1},
143     {0x1.1ec8668ecaceep-55, 0x1.fc26470e19fd3p-1},
144     {-0x1.87df6378811c7p-55, 0x1.fd88da3d12526p-1},
145     {0x1.521ecd0c67e35p-57, 0x1.fe9cdad01883ap-1},
146     {-0x1.c57bc2e24aa15p-57, 0x1.ff621e3796d7ep-1},
147     {-0x1.1354d4556e4cbp-55, 0x1.ffd886084cd0dp-1},
148     {0, 1},
149 #ifndef LIBC_MATH_HAS_SMALL_TABLES
150     {-0x1.1354d4556e4cbp-55, 0x1.ffd886084cd0dp-1},
151     {-0x1.c57bc2e24aa15p-57, 0x1.ff621e3796d7ep-1},
152     {0x1.521ecd0c67e35p-57, 0x1.fe9cdad01883ap-1},
153     {-0x1.87df6378811c7p-55, 0x1.fd88da3d12526p-1},
154     {0x1.1ec8668ecaceep-55, 0x1.fc26470e19fd3p-1},
155     {-0x1.7a0a8ca13571fp-55, 0x1.fa7557f08a517p-1},
156     {0x1.ab256778ffcb6p-56, 0x1.f8764fa714ba9p-1},
157     {0x1.562172a361fd3p-56, 0x1.f6297cff75cbp-1},
158     {-0x1.d7bafb51f72e6p-56, 0x1.f38f3ac64e589p-1},
159     {0x1.52c7adc6b4989p-56, 0x1.f0a7efb9230d7p-1},
160     {0x1.e82c791f59cc2p-56, 0x1.ed740e7684963p-1},
161     {0x1.760b1e2e3f81ep-55, 0x1.e9f4156c62ddap-1},
162     {-0x1.16b56f2847754p-57, 0x1.e6288ec48e112p-1},
163     {-0x1.014c76c126527p-55, 0x1.e212104f686e5p-1},
164     {0x1.83c37c6107db3p-55, 0x1.ddb13b6ccc23cp-1},
165     {0x1.457e610231ac2p-56, 0x1.d906bcf328d46p-1},
166     {-0x1.4ef5295d25af2p-55, 0x1.d4134d14dc93ap-1},
167     {-0x1.e7b6bb5ab58aep-58, 0x1.ced7af43cc773p-1},
168     {-0x1.2fb761e946603p-58, 0x1.c954b213411f5p-1},
169     {-0x1.6e0b1757c8d07p-56, 0x1.c38b2f180bdb1p-1},
170     {-0x1.825a732ac700ap-55, 0x1.bd7c0ac6f952ap-1},
171     {-0x1.bc69f324e6d61p-55, 0x1.b728345196e3ep-1},
172     {-0x1.926da300ffccep-55, 0x1.b090a581502p-1},
173     {0x1.9f630e8b6dac8p-60, 0x1.a9b66290ea1a3p-1},
174     {-0x1.128bb015df175p-56, 0x1.a29a7a0462782p-1},
175     {-0x1.30ee286712474p-55, 0x1.9b3e047f38741p-1},
176     {0x1.3d419a920df0bp-55, 0x1.93a22499263fbp-1},
177     {-0x1.2c5e12ed1336dp-55, 0x1.8bc806b151741p-1},
178     {-0x1.6f420f8ea3475p-56, 0x1.83b0e0bff976ep-1},
179     {-0x1.0f537acdf0ad7p-56, 0x1.7b5df226aafafp-1},
180     {0x1.0d4ef0f1d915cp-55, 0x1.72d0837efff96p-1},
181     {-0x1.bdd3413b26456p-55, 0x1.6a09e667f3bcdp-1},
182     {-0x1.251b352ff2a37p-56, 0x1.610b7551d2cdfp-1},
183     {-0x1.75720992bfbb2p-55, 0x1.57d69348cecap-1},
184     {0x1.3c293edceb327p-57, 0x1.4e6cabbe3e5e9p-1},
185     {0x1.8076a2cfdc6b3p-57, 0x1.44cf325091dd6p-1},
186     {0x1.e3e25e3954964p-56, 0x1.3affa292050b9p-1},
187     {-0x1.efcc626f74a6fp-57, 0x1.30ff7fce17035p-1},
188     {-0x1.5da743ef3770cp-55, 0x1.26d054cdd12dfp-1},
189     {0x1.b25dd267f66p-55, 0x1.1c73b39ae68c8p-1},
190     {-0x1.ef23b69abe4f1p-55, 0x1.11eb3541b4b23p-1},
191     {-0x1.a5a014347406cp-55, 0x1.073879922ffeep-1},
192     {-0x1.2ec1fc1b776b8p-60, 0x1.f8ba4dbf89abap-2},
193     {0x1.e0d891d3c6841p-58, 0x1.e2b5d3806f63bp-2},
194     {0x1.6850e59c37f8fp-58, 0x1.cc66e9931c45ep-2},
195     {0x1.5b362cb974183p-57, 0x1.b5d1009e15ccp-2},
196     {0x1.6da81290bdbabp-57, 0x1.9ef7943a8ed8ap-2},
197     {-0x1.72cedd3d5a61p-57, 0x1.87de2a6aea963p-2},
198     {-0x1.44b19e0864c5dp-56, 0x1.7088530fa459fp-2},
199     {-0x1.efdc0d58cf62p-62, 0x1.58f9a75ab1fddp-2},
200     {0x1.0c97c4afa2518p-56, 0x1.4135c94176601p-2},
201     {-0x1.5d28da2c4612dp-56, 0x1.294062ed59f06p-2},
202     {0x1.824c20ab7aa9ap-56, 0x1.111d262b1f677p-2},
203     {-0x1.42deef11da2c4p-57, 0x1.f19f97b215f1bp-3},
204     {-0x1.af1439e521935p-62, 0x1.c0b826a7e4f63p-3},
205     {-0x1.26d19b9ff8d82p-57, 0x1.8f8b83c69a60bp-3},
206     {0x1.531ff779ddac6p-57, 0x1.5e214448b3fc6p-3},
207     {0x1.13000a89a11ep-58, 0x1.2c8106e8e613ap-3},
208     {0x1.a2704729ae56dp-59, 0x1.f564e56a9730ep-4},
209     {-0x1.e2718d26ed688p-60, 0x1.917a6bc29b42cp-4},
210     {-0x1.9a088a8bf6b2cp-59, 0x1.2d52092ce19f6p-4},
211     {-0x1.912bd0d569a9p-61, 0x1.91f65f10dd814p-5},
212     {-0x1.b1d63091a013p-64, 0x1.92155f7a3667ep-6},
213     {0, 0},
214     {0x1.b1d63091a013p-64, -0x1.92155f7a3667ep-6},
215     {0x1.912bd0d569a9p-61, -0x1.91f65f10dd814p-5},
216     {0x1.9a088a8bf6b2cp-59, -0x1.2d52092ce19f6p-4},
217     {0x1.e2718d26ed688p-60, -0x1.917a6bc29b42cp-4},
218     {-0x1.a2704729ae56dp-59, -0x1.f564e56a9730ep-4},
219     {-0x1.13000a89a11ep-58, -0x1.2c8106e8e613ap-3},
220     {-0x1.531ff779ddac6p-57, -0x1.5e214448b3fc6p-3},
221     {0x1.26d19b9ff8d82p-57, -0x1.8f8b83c69a60bp-3},
222     {0x1.af1439e521935p-62, -0x1.c0b826a7e4f63p-3},
223     {0x1.42deef11da2c4p-57, -0x1.f19f97b215f1bp-3},
224     {-0x1.824c20ab7aa9ap-56, -0x1.111d262b1f677p-2},
225     {0x1.5d28da2c4612dp-56, -0x1.294062ed59f06p-2},
226     {-0x1.0c97c4afa2518p-56, -0x1.4135c94176601p-2},
227     {0x1.efdc0d58cf62p-62, -0x1.58f9a75ab1fddp-2},
228     {0x1.44b19e0864c5dp-56, -0x1.7088530fa459fp-2},
229     {0x1.72cedd3d5a61p-57, -0x1.87de2a6aea963p-2},
230     {-0x1.6da81290bdbabp-57, -0x1.9ef7943a8ed8ap-2},
231     {-0x1.5b362cb974183p-57, -0x1.b5d1009e15ccp-2},
232     {-0x1.6850e59c37f8fp-58, -0x1.cc66e9931c45ep-2},
233     {-0x1.e0d891d3c6841p-58, -0x1.e2b5d3806f63bp-2},
234     {0x1.2ec1fc1b776b8p-60, -0x1.f8ba4dbf89abap-2},
235     {0x1.a5a014347406cp-55, -0x1.073879922ffeep-1},
236     {0x1.ef23b69abe4f1p-55, -0x1.11eb3541b4b23p-1},
237     {-0x1.b25dd267f66p-55, -0x1.1c73b39ae68c8p-1},
238     {0x1.5da743ef3770cp-55, -0x1.26d054cdd12dfp-1},
239     {0x1.efcc626f74a6fp-57, -0x1.30ff7fce17035p-1},
240     {-0x1.e3e25e3954964p-56, -0x1.3affa292050b9p-1},
241     {-0x1.8076a2cfdc6b3p-57, -0x1.44cf325091dd6p-1},
242     {-0x1.3c293edceb327p-57, -0x1.4e6cabbe3e5e9p-1},
243     {0x1.75720992bfbb2p-55, -0x1.57d69348cecap-1},
244     {0x1.251b352ff2a37p-56, -0x1.610b7551d2cdfp-1},
245     {0x1.bdd3413b26456p-55, -0x1.6a09e667f3bcdp-1},
246     {-0x1.0d4ef0f1d915cp-55, -0x1.72d0837efff96p-1},
247     {0x1.0f537acdf0ad7p-56, -0x1.7b5df226aafafp-1},
248     {0x1.6f420f8ea3475p-56, -0x1.83b0e0bff976ep-1},
249     {0x1.2c5e12ed1336dp-55, -0x1.8bc806b151741p-1},
250     {-0x1.3d419a920df0bp-55, -0x1.93a22499263fbp-1},
251     {0x1.30ee286712474p-55, -0x1.9b3e047f38741p-1},
252     {0x1.128bb015df175p-56, -0x1.a29a7a0462782p-1},
253     {-0x1.9f630e8b6dac8p-60, -0x1.a9b66290ea1a3p-1},
254     {0x1.926da300ffccep-55, -0x1.b090a581502p-1},
255     {0x1.bc69f324e6d61p-55, -0x1.b728345196e3ep-1},
256     {0x1.825a732ac700ap-55, -0x1.bd7c0ac6f952ap-1},
257     {0x1.6e0b1757c8d07p-56, -0x1.c38b2f180bdb1p-1},
258     {0x1.2fb761e946603p-58, -0x1.c954b213411f5p-1},
259     {0x1.e7b6bb5ab58aep-58, -0x1.ced7af43cc773p-1},
260     {0x1.4ef5295d25af2p-55, -0x1.d4134d14dc93ap-1},
261     {-0x1.457e610231ac2p-56, -0x1.d906bcf328d46p-1},
262     {-0x1.83c37c6107db3p-55, -0x1.ddb13b6ccc23cp-1},
263     {0x1.014c76c126527p-55, -0x1.e212104f686e5p-1},
264     {0x1.16b56f2847754p-57, -0x1.e6288ec48e112p-1},
265     {-0x1.760b1e2e3f81ep-55, -0x1.e9f4156c62ddap-1},
266     {-0x1.e82c791f59cc2p-56, -0x1.ed740e7684963p-1},
267     {-0x1.52c7adc6b4989p-56, -0x1.f0a7efb9230d7p-1},
268     {0x1.d7bafb51f72e6p-56, -0x1.f38f3ac64e589p-1},
269     {-0x1.562172a361fd3p-56, -0x1.f6297cff75cbp-1},
270     {-0x1.ab256778ffcb6p-56, -0x1.f8764fa714ba9p-1},
271     {0x1.7a0a8ca13571fp-55, -0x1.fa7557f08a517p-1},
272     {-0x1.1ec8668ecaceep-55, -0x1.fc26470e19fd3p-1},
273     {0x1.87df6378811c7p-55, -0x1.fd88da3d12526p-1},
274     {-0x1.521ecd0c67e35p-57, -0x1.fe9cdad01883ap-1},
275     {0x1.c57bc2e24aa15p-57, -0x1.ff621e3796d7ep-1},
276     {0x1.1354d4556e4cbp-55, -0x1.ffd886084cd0dp-1},
277     {0, -1},
278     {0x1.1354d4556e4cbp-55, -0x1.ffd886084cd0dp-1},
279     {0x1.c57bc2e24aa15p-57, -0x1.ff621e3796d7ep-1},
280     {-0x1.521ecd0c67e35p-57, -0x1.fe9cdad01883ap-1},
281     {0x1.87df6378811c7p-55, -0x1.fd88da3d12526p-1},
282     {-0x1.1ec8668ecaceep-55, -0x1.fc26470e19fd3p-1},
283     {0x1.7a0a8ca13571fp-55, -0x1.fa7557f08a517p-1},
284     {-0x1.ab256778ffcb6p-56, -0x1.f8764fa714ba9p-1},
285     {-0x1.562172a361fd3p-56, -0x1.f6297cff75cbp-1},
286     {0x1.d7bafb51f72e6p-56, -0x1.f38f3ac64e589p-1},
287     {-0x1.52c7adc6b4989p-56, -0x1.f0a7efb9230d7p-1},
288     {-0x1.e82c791f59cc2p-56, -0x1.ed740e7684963p-1},
289     {-0x1.760b1e2e3f81ep-55, -0x1.e9f4156c62ddap-1},
290     {0x1.16b56f2847754p-57, -0x1.e6288ec48e112p-1},
291     {0x1.014c76c126527p-55, -0x1.e212104f686e5p-1},
292     {-0x1.83c37c6107db3p-55, -0x1.ddb13b6ccc23cp-1},
293     {-0x1.457e610231ac2p-56, -0x1.d906bcf328d46p-1},
294     {0x1.4ef5295d25af2p-55, -0x1.d4134d14dc93ap-1},
295     {0x1.e7b6bb5ab58aep-58, -0x1.ced7af43cc773p-1},
296     {0x1.2fb761e946603p-58, -0x1.c954b213411f5p-1},
297     {0x1.6e0b1757c8d07p-56, -0x1.c38b2f180bdb1p-1},
298     {0x1.825a732ac700ap-55, -0x1.bd7c0ac6f952ap-1},
299     {0x1.bc69f324e6d61p-55, -0x1.b728345196e3ep-1},
300     {0x1.926da300ffccep-55, -0x1.b090a581502p-1},
301     {-0x1.9f630e8b6dac8p-60, -0x1.a9b66290ea1a3p-1},
302     {0x1.128bb015df175p-56, -0x1.a29a7a0462782p-1},
303     {0x1.30ee286712474p-55, -0x1.9b3e047f38741p-1},
304     {-0x1.3d419a920df0bp-55, -0x1.93a22499263fbp-1},
305     {0x1.2c5e12ed1336dp-55, -0x1.8bc806b151741p-1},
306     {0x1.6f420f8ea3475p-56, -0x1.83b0e0bff976ep-1},
307     {0x1.0f537acdf0ad7p-56, -0x1.7b5df226aafafp-1},
308     {-0x1.0d4ef0f1d915cp-55, -0x1.72d0837efff96p-1},
309     {0x1.bdd3413b26456p-55, -0x1.6a09e667f3bcdp-1},
310     {0x1.251b352ff2a37p-56, -0x1.610b7551d2cdfp-1},
311     {0x1.75720992bfbb2p-55, -0x1.57d69348cecap-1},
312     {-0x1.3c293edceb327p-57, -0x1.4e6cabbe3e5e9p-1},
313     {-0x1.8076a2cfdc6b3p-57, -0x1.44cf325091dd6p-1},
314     {-0x1.e3e25e3954964p-56, -0x1.3affa292050b9p-1},
315     {0x1.efcc626f74a6fp-57, -0x1.30ff7fce17035p-1},
316     {0x1.5da743ef3770cp-55, -0x1.26d054cdd12dfp-1},
317     {-0x1.b25dd267f66p-55, -0x1.1c73b39ae68c8p-1},
318     {0x1.ef23b69abe4f1p-55, -0x1.11eb3541b4b23p-1},
319     {0x1.a5a014347406cp-55, -0x1.073879922ffeep-1},
320     {0x1.2ec1fc1b776b8p-60, -0x1.f8ba4dbf89abap-2},
321     {-0x1.e0d891d3c6841p-58, -0x1.e2b5d3806f63bp-2},
322     {-0x1.6850e59c37f8fp-58, -0x1.cc66e9931c45ep-2},
323     {-0x1.5b362cb974183p-57, -0x1.b5d1009e15ccp-2},
324     {-0x1.6da81290bdbabp-57, -0x1.9ef7943a8ed8ap-2},
325     {0x1.72cedd3d5a61p-57, -0x1.87de2a6aea963p-2},
326     {0x1.44b19e0864c5dp-56, -0x1.7088530fa459fp-2},
327     {0x1.efdc0d58cf62p-62, -0x1.58f9a75ab1fddp-2},
328     {-0x1.0c97c4afa2518p-56, -0x1.4135c94176601p-2},
329     {0x1.5d28da2c4612dp-56, -0x1.294062ed59f06p-2},
330     {-0x1.824c20ab7aa9ap-56, -0x1.111d262b1f677p-2},
331     {0x1.42deef11da2c4p-57, -0x1.f19f97b215f1bp-3},
332     {0x1.af1439e521935p-62, -0x1.c0b826a7e4f63p-3},
333     {0x1.26d19b9ff8d82p-57, -0x1.8f8b83c69a60bp-3},
334     {-0x1.531ff779ddac6p-57, -0x1.5e214448b3fc6p-3},
335     {-0x1.13000a89a11ep-58, -0x1.2c8106e8e613ap-3},
336     {-0x1.a2704729ae56dp-59, -0x1.f564e56a9730ep-4},
337     {0x1.e2718d26ed688p-60, -0x1.917a6bc29b42cp-4},
338     {0x1.9a088a8bf6b2cp-59, -0x1.2d52092ce19f6p-4},
339     {0x1.912bd0d569a9p-61, -0x1.91f65f10dd814p-5},
340     {0x1.b1d63091a013p-64, -0x1.92155f7a3667ep-6},
341 #endif // !LIBC_MATH_HAS_SMALL_TABLES
342 };
343 
344 } // namespace LIBC_NAMESPACE_DECL
345 
346 #endif // LLVM_LIBC_SRC_MATH_GENERIC_RANGE_REDUCTION_DOUBLE_FMA_H
347